Classification of Solvable Feynman Path Integrals

TL;DR

This paper provides a systematic classification and a comprehensive table of solvable Feynman path integrals in quantum mechanics, highlighting recent progress and foundational formulas since Feynman's original work.

Contribution

It introduces a general theory and explicit formulas for basic path integrals, enabling classification and calculation of solvable path integrals in quantum mechanics.

Findings

Compilation of a table of solvable path integrals

Development of a general classification scheme

Presentation of explicit formulas for basic path integrals

Abstract

A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given. Explicit formul\ae\ for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based.